#### Answer

54 cm

#### Work Step by Step

The diagram consist of two right triangles ADB and BDC
By pythagoras theorem on ADB
$AD^{2}$ =$DB^{2}$ + $AB^{2}$
$20^{2}$ = $DB^{2}$ + $16^{2}$
400 = $DB^{2}$+ 256
$DB^{2}$ = 400 - 256
$DB^{2}$ = 144
DB = 12
By pythagoras theorem on DBC
$CB^{2}$ =$DB^{2}$ + $DC^{2}$
$CB^{2}$ = $12^{2}$ + $5^{2}$
$CB^{2}$ = 144 + 25
$CB^{2}$ = 169
CB = 13
The perimeter of ABCD = AB + BC+CD+DA
= 20 +5 + 13 + 16
=54 cm